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Question Number 213459 by golsendro last updated on 06/Nov/24

Find tupple natural numbers (a,b,c) such that { ((max{((a+b)/2)+((∣a−b∣)/2) , ((b+c)/2)+((∣b−c∣)/2) ,((c+a)/2)+((∣c−a∣)/2)}=a)),((min{((a+b)/2)−((∣a−b∣)/2) , ((b+c)/2)−((∣b−c∣)/2) , ((c+a)/2)−((∣c−a∣)/2)}=b)) :} where a+b+c = 10

Findtupplenaturalnumbers(a,b,c)suchthat{max{a+b2+∣a−b∣2,b+c2+∣b−c∣2,c+a2+∣c−a∣2}=amin{a+b2−∣a−b∣2,b+c2−∣b−c∣2,c+a2−∣c−a∣2}=bwherea+b+c=10

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